Thousands more police officers are to undergo riot training, it emerged on Monday, as David Cameron pledged to tackle 120,000 of the country's most "troubled families" as part of the coalition's "social and security fightback" against the "slow-motion moral collapse" of Britain.

The prime minister ruled out race, poverty and spending cuts as factors behind last week's riots, but showed signs of wanting to look deeper into their causes by acceding to Labour's demands for a public inquiry.

As part of the "security fightback" section of the government's response, the home secretary, Theresa May, wrote to Sir Denis O'Connor, HM's chief inspector of constabulary, asking for clearer guidance for forces on their preparations to tackle riots. Senior officers said that they did not have sufficient number of officers trained in riot control to respond immediately to last week's events, but Home Office sources confirmed on Monday night that they now expected a big expansion in riot training for the police as a result of May's request.

"I have asked him to provide clearer guidance to forces about the size of deployments, the need for mutual aid, pre-emptive action, public order tactics, the number of officers trained in public order policing, and appropriate arrests policy," the home secretary is to announce on Tuesday in a speech detailing the "security fightback".

As part of the "social fightback", Cameron had a tough-love message for 120,000 of the UK's most "troubled families". He set himself the rigid target of the next election to put all of them through some kind of family-intervention programme.

In a speech setting out his analysis of what led to the riots, Cameron highlighted those families across the UK who were dealing with multiple complex social health and economic problems. Lifting them out of extreme worklessness would be regarded as a measure of his success in his wider agenda of fixing Britain's broken society, he said. Cameron said he would put "rocket boosters" on attempts to rehabilitate those 120,000.

Speaking at a youth centre in his Witney constituency in Oxfordshire, Cameron said: "The broken society is back at the top of my political agenda … I have an ambition, before the end of this parliament, we will turn around the lives of 120,000 most troubled families … we need more urgent action on the families that some people call 'problem', others call 'troubled'. The ones everyone in their neighbourhood knows and often avoids."

He said would ask the chief executive of an organisation called Action for Employment (A4e), Emma Harrison, who he appointed his "families champion" in December, to use her experience in dealing with troubled families in three pilot areas to overcome the bureaucratic problems that have prevented the rapid expansion of Labour's similar families intervention programme, running since 2006.

A former coalition government adviser, Dame Clare Tickell, head of Action for Children, which runs some family intervention projects, later told BBC Radio 4 that she was concerned about funding for the intervention. Ringfencing was scrapped last May.

In 2008 Gordon Brown promised to target "more than 110,000 problem families with disruptive young people". The latest official figures show that in 2009-10 only 3,518 families were actually in the intervention programme and it has helped only 7,300 families since being set up in 2006.

While the intent of Cameron's pledge received cautious cross-party support, Labour echoed Tickell's concerns and doubted whether it could be funded.

Matt Cavanagh, of the Institute for Public Policy Research and one of the Labour advisers who helped draft the policy when the party was in power, suggested it would require £100m a year over the next four years. "Local authorities used to part-fund [these programmes] but the government has dismantled all the ringfences and given LAs more autonomy in their reduced budgets. The result for problem family programmes has been neglect and confusion, as ministers now seem to admit."

While the government said it would make available £200m from the European Social Fund to help fund the target, the rest would come from the early intervention grant, which is to be cut by 11% by next year and has funding for Sure Start, teenage pregnancy and youth centres to meet. Labour said Sure Start had been cut by 20%. A government source acknowledged that using these resources to fund Cameron's target could vary. They said: "It is for local authorities and their partners, including the voluntary sector, to decide how much they wish to prioritise on families with multiple problems in their area."